By Mikhail I. Ostrovskii

Embeddings of discrete metric areas into Banach areas lately turned a massive instrument in machine technological know-how and topology. The publication can assist readers to go into and to paintings during this very swiftly constructing zone having many very important connections with assorted elements of arithmetic and desktop technological know-how.

The function of the publication is to provide probably the most vital recommendations and effects, totally on bilipschitz and coarse embeddings. the subjects comprise embeddability of in the neighborhood finite metric areas into Banach areas is finitely made up our minds, buildings of embeddings, distortion when it comes to Poincare inequalities, buildings of households of expanders and of households of graphs with unbounded girth and reduce bounds on common levels, Banach areas which don't admit coarse embeddings of expanders, constitution of metric areas which aren't coarsely embeddable right into a Hilbert area, functions of Markov chains to embeddability challenge, metric characterizations of houses of Banach areas, and Lipschitz loose spaces."

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